Search results for "MSC: 34A60"

showing 3 items of 3 documents

Constrained differential inclusions with nonlocal initial conditions

2017

International audience; We show existence for the perturbed sweeping process with nonlocal initial conditions under very general hypotheses. Periodic, anti-periodic, mean value and multipoints conditions are included in this study. We give abstract results for differential inclusions with nonlocal initial conditions through bounding functions and tangential conditions. Some applications to differential complementarity systems and to vector hysteresis are given.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]MSC: 34A60 49J52 34G25 49J53 34B10Periodic solutionsNonlocal Cauchy problemDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC][MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Sweeping processesNormal coneBounding functions
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Differential inclusions involving normal cones of nonregular sets in Hilbert spaces

2017

This thesis is dedicated to the study of differential inclusions involving normal cones of nonregular sets in Hilbert spaces. In particular, we are interested in the sweeping process and its variants. The sweeping process is a constrained differential inclusion involving normal cones which appears naturally in several applications such as elastoplasticity, electrical circuits, hysteresis, crowd motion, etc.This work is divided conceptually in three parts: Study of positively alpha-far sets, existence results for differential inclusions involving normal cones and characterizations of Lyapunov pairs for the sweeping process. In the first part (Chapter 2), we investigate the class of positivel…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]cône normalMoreau-Yosida regularizationcono normalmétodo de tipo Galerkinfonction distanceGalerkin-like methodMSC: 34A60 49J52 34G25 49J53 34B10 93D30subdiferencial de Clarkeprocessus de rafleInclusión diferencialensembles positivement alpha-far'sweeping processfonctions de Lyapunovsous-différentiel de Clarkeprocesos de arrastrefunción distanciaLyapunov functionsconjuntos positivamente alpha-farFunciones de Lyapunovméthode de type Galerkinrégularisation de Moreau-YosidaDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Clarke subdifferentialregularización de Moreau-YosidaDistance functionInclusion différentielle[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Normal conepositively alpha-far sets
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Regularization of perturbed state-dependent sweeping processes with nonregular sets

2018

International audience; In this paper, we prove the convergence strongly pointwisely (up to a subsequence) of Moreau-Yosida regularization of perturbed state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets in separable Hilbert spaces. Some relevant consequences are indicated.

Positively alpha-far sets[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]MSC: 34A60 49J52 34G25 49J53Moreau-Yosida regularizationDifferential inclusions[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Subsmooth setsSweeping processClarke normal cone
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